5.

Consider the parametric equations below' x:1+3t, yzzrz (a) Sketch the curve by using the parametric equations to piot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve. Find a formula for the general term an of the sequence, assuming that the pattern of the first fem.I terms continues. (Assume that n begins with 1.) {1_1 1_1 1 } ' 2'4' 8'16"" Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, enter DIVERGES.} _ 3 anco I lima = nzo-J n Determine whether the sequence converges or diverges. If it converges, find the limit. {If the quantity diverges, enter DIVERGES.) _ (1)!" +2n3 an 3 n +5n2+6 Determine whether the sequence converges or diverges. If it converges, find the limit. {If the sequence diverges, enter DIVERGES.} 3+7'n2 a." : n+3n2 .".'3:r.' 'n' Determine whether the integral is convergent or divergent. [f it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) C 2' 4 dz .392 + 4 Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y' Draw a typical approximating rectangle. y:x34x, y:51 )i 0 Find the area or the region. Sketch the region enclused by the given curves. Decide whethertu integrate with respect to x or y' Draw a typical approximating rectangle. y:3x, y:5XZX2 Find the area of the region